Evolutionary multi-objective optimization (EMO) algorithms have been demonstrated to be effective in solving multi-criteria decision-making problems. In real-world applications, analysts often employ several algorithms concurrently and compare their solution sets to gain insight into the characteristics of different algorithms and explore a broader range of feasible solutions. However, EMO algorithms are typically treated as black boxes, leading to difficulties in performing detailed analysis and comparisons between the internal evolutionary processes. Inspired by the successful application of visual analytics tools in explainable AI, we argue that interactive visualization can significantly enhance the comparative analysis between multiple EMO algorithms. In this paper, we present a visual analytics framework that enables the exploration and comparison of evolutionary processes in EMO algorithms. Guided by a literature review and expert interviews, the proposed framework addresses various analytical tasks and establishes a multi-faceted visualization design to support the comparative analysis of intermediate generations in the evolution as well as solution sets. We demonstrate the effectiveness of our framework through case studies on benchmarking and real-world multi-objective optimization problems to elucidate how analysts can leverage our framework to inspect and compare diverse algorithms.

We investigate the problem of compound estimation of normal means while accounting for the presence of side information. Leveraging the empirical Bayes framework, we develop a nonparametric integrative Tweedie (NIT) approach that incorporates structural knowledge encoded in multivariate auxiliary data to enhance the precision of compound estimation. Our approach employs convex optimization tools to estimate the gradient of the log-density directly, enabling the incorporation of structural constraints. We conduct theoretical analyses of the asymptotic risk of NIT and establish the rate at which NIT converges to the oracle estimator. As the dimension of the auxiliary data increases, we accurately quantify the improvements in estimation risk and the associated deterioration in convergence rate. The numerical performance of NIT is illustrated through the analysis of both simulated and real data, demonstrating its superiority over existing methods.

In the past few years, there has been considerable interest in two prominent approaches for Distributionally Robust Optimization (DRO): Divergence-based and Wasserstein-based methods. The divergence approach models misspecification in terms of likelihood ratios, while the latter models it through a measure of distance or cost in actual outcomes. Building upon these advances, this paper introduces a novel approach that unifies these methods into a single framework based on optimal transport (OT) with conditional moment constraints. Our proposed approach, for example, makes it possible for optimal adversarial distributions to simultaneously perturb likelihood and outcomes, while producing an optimal (in an optimal transport sense) coupling between the baseline model and the adversarial model.Additionally, the paper investigates several duality results and presents tractable reformulations that enhance the practical applicability of this unified framework.

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for overdispersed count data, for example, and allows for categorical or grouped covariates as well as continuous covariates. A randomized group-regularized optimization problem is studied. The added randomization allows us to construct a post-selection likelihood which we show to be adequate for selective inference when conditioning on the event of the selection of the grouped covariates. This likelihood also provides a selective point estimator, accounting for the selection by the group lasso. Confidence regions for the regression parameters in the selected model take the form of Wald-type regions and are shown to have bounded volume. The selective inference method for grouped lasso is illustrated on data from the national health and nutrition examination survey while simulations showcase its behaviour and favorable comparison with other methods.

This paper provides an overview of the historical progression of distributed optimization techniques, tracing their development from early duality-based methods pioneered by Dantzig, Wolfe, and Benders in the 1960s to the emergence of the Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) algorithm. The initial focus on Lagrangian relaxation for convex problems and decomposition strategies led to the refinement of methods like the Alternating Direction Method of Multipliers (ADMM). The resurgence of interest in distributed optimization in the late 2000s, particularly in machine learning and imaging, demonstrated ADMM's practical efficacy and its unifying potential. This overview also highlights the emergence of the proximal center method and its applications in diverse domains. Furthermore, the paper underscores the distinctive features of ALADIN, which offers convergence guarantees for non-convex scenarios without introducing auxiliary variables, differentiating it from traditional augmentation techniques. In essence, this work encapsulates the historical trajectory of distributed optimization and underscores the promising prospects of ALADIN in addressing non-convex optimization challenges.

In this paper, the problem of drone-assisted collaborative learning is considered. In this scenario, swarm of intelligent wireless devices train a shared neural network (NN) model with the help of a drone. Using its sensors, each device records samples from its environment to gather a local dataset for training. The training data is severely heterogeneous as various devices have different amount of data and sensor noise level. The intelligent devices iteratively train the NN on their local datasets and exchange the model parameters with the drone for aggregation. For this system, the convergence rate of collaborative learning is derived while considering data heterogeneity, sensor noise levels, and communication errors, then, the drone trajectory that maximizes the final accuracy of the trained NN is obtained. The proposed trajectory optimization approach is aware of both the devices data characteristics (i.e., local dataset size and noise level) and their wireless channel conditions, and significantly improves the convergence rate and final accuracy in comparison with baselines that only consider data characteristics or channel conditions. Compared to state-of-the-art baselines, the proposed approach achieves an average 3.85% and 3.54% improvement in the final accuracy of the trained NN on benchmark datasets for image recognition and semantic segmentation tasks, respectively. Moreover, the proposed framework achieves a significant speedup in training, leading to an average 24% and 87% saving in the drone hovering time, communication overhead, and battery usage, respectively for these tasks.

Developing extended hydrodynamics equations valid for both dense and rarefied gases remains a great challenge. A systematical solution for this challenge is the moment method describing both dense and rarefied gas behaviors with moments of gas molecule velocity distributions. Among moment methods, the maximal entropy moment method (MEM) stands out for its well-posedness and stability, which utilizes velocity distributions with maximized entropy. However, finding such distributions requires solving an ill-conditioned and computation-demanding optimization problem. This problem causes numerical overflow and breakdown when the numerical precision is insufficient, especially for flows like high-speed shock waves. It also prevents modern GPUs from accelerating optimization with their enormous single floating-point precision computation power. This paper aims to stabilize MEM, making it practical for simulating very strong normal shock waves on modern GPUs at single precision. We propose the gauge transformations for MEM, making the optimization less ill-conditioned. We also tackle numerical overflow and breakdown by adopting the canonical form of distribution and Newton's modified optimization method. With these techniques, we achieved a single-precision GPU simulation of a Mach 10 shock wave with 35 moments MEM, surpassing the previous double-precision results of Mach 4. Moreover, we argued that over-refined spatial mesh degrades both the accuracy and stability of MEM. Overall, this paper makes the maximal entropy moment method practical for simulating very strong normal shock waves on modern GPUs at single-precision, with significant stability improvement compared to previous methods.

Shape morphing that transforms morphologies in response to stimuli is crucial for future multifunctional systems. While kirigami holds great promise in enhancing shape-morphing, existing designs primarily focus on kinematics and overlook the underlying physics. This study introduces a differentiable inverse design framework that considers the physical interplay between geometry, materials, and stimuli of active kirigami, made by soft material embedded with magnetic particles, to realize target shape-morphing upon magnetic excitation. We achieve this by combining differentiable kinematics and energy models into a constrained optimization, simultaneously designing the cuts and magnetization orientations to ensure kinematic and physical feasibility. Complex kirigami designs are obtained automatically with unparallel efficiency, which can be remotely controlled to morph into intricate target shapes and even multiple states. The proposed framework can be extended to accommodate various active systems, bridging geometry and physics to push the frontiers in shape-morphing applications, like flexible electronics and minimally invasive surgery.

Federated learning (FL) has found many successes in wireless networks; however, the implementation of FL has been hindered by the energy limitation of mobile devices (MDs) and the availability of training data at MDs. How to integrate wireless power transfer and mobile crowdsensing towards sustainable FL solutions is a research topic entirely missing from the open literature. This work for the first time investigates a resource allocation problem in collaborative sensing-assisted sustainable FL (S2FL) networks with the goal of minimizing the total completion time. We investigate a practical harvesting-sensing-training-transmitting protocol in which energy-limited MDs first harvest energy from RF signals, use it to gain a reward for user participation, sense the training data from the environment, train the local models at MDs, and transmit the model updates to the server. The total completion time minimization problem of jointly optimizing power transfer, transmit power allocation, data sensing, bandwidth allocation, local model training, and data transmission is complicated due to the non-convex objective function, highly non-convex constraints, and strongly coupled variables. We propose a computationally-efficient path-following algorithm to obtain the optimal solution via the decomposition technique. In particular, inner convex approximations are developed for the resource allocation subproblem, and the subproblems are performed alternatively in an iterative fashion. Simulation results are provided to evaluate the effectiveness of the proposed S2FL algorithm in reducing the completion time up to 21.45% in comparison with other benchmark schemes. Further, we investigate an extension of our work from frequency division multiple access (FDMA) to non-orthogonal multiple access (NOMA) and show that NOMA can speed up the total completion time 8.36% on average of the considered FL system.

Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and appropriate differential terms, algorithms can autonomously uncover equations from data. This paper explores the prerequisites and tools for independent equation discovery without expert input, eliminating the need for equation form assumptions. We focus on addressing the challenge of assessing the adequacy of discovered equations when the correct equation is unknown, with the aim of providing insights for reliable equation discovery without prior knowledge of the equation form.